Question

Two numbers differ by 4. The product of the two numbers is 221. What are the numbers?

Answer 1

Answer:

let the number x and y

x - y = 4 \\ xy = 221 \\ x =  \frac{221}{y}  \\  \frac{221}{y}  - y = 4 \\ 221 -  {y}^{2}  = 4y \\  -  {y}^{2}  - 4y + 221 = 0 \\  {y}^{2}  + 4y - 221 = 0 \\  {y}^{2}  - 17y + 13y - 221 = 0 \\ y(y - 17) + 13(y - 17) = 0 \\ (y + 13)(y - 17) = 0 \\ y =  - 13 \\ y = 17 \\  

put these values of y into any of the equation.

xy= 221

x =  \frac{221}{ - 13}  =  - 17 \\ x =  \frac{221}{17 }  = 13

Step-by-step explanation: